Dimensionality reduction techniques, mapping high-dimensional data into a low-dimensional space, can alleviate the curse of dimensionality (e.g., the difficulty in estimating the variable importance) and other undesired properties (e.g., the sparse high dimensional space) of high-dimensional data analysis [1]}, [2]}, [3]}. Dimensionality reduction is crucial in many domains, such as biological engineering and material science [1]}. However, dimensionality reduction techniques are limited due to the lack of interpretability and connectivity to the original physical variables. Even after extracting low-dimensional features, it is difficult to determine which physical variables are important as the features being artificial. In engineering applications, identifying influential physical variables is critical since it provides ways to reduce the number of occasions in operational controls and experimental designs to consider for determining the optimal policy. Variable selection, also referred to as model selection or feature selection, is a good alternative to the dimensionality reduction because this technique can pinpoint which physical variables are important by producing a subset of the original variables that are significant [5]}. Variable selection typically involves a heuristic search, so important interactions between physical variables can easily be missed. In addition, some backward selection approaches begin with a full-dimensional model which are not free of the curse of dimensionality.
